Subgroups — C₅×#86922 #14484153

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5734	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5728	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5694	C₂	1	2	yes	maximal, complemented
5	C₅×#5691	C₂	1	2	yes	maximal, complemented
6	C₅×#5642	C₂	1	2	yes	maximal, complemented
7	C₅×#5637	C₂	1	4	yes	maximal, complemented
8	C₅×#5627	C₂	1	2	yes	maximal, complemented
9	C₅×#5624	C₂	1	4	yes	maximal, complemented
10	C₅×#5584	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#239	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5555	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5554	C₂	1	2	yes	maximal, complemented
14	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×#237	C₂	1	2	yes	maximal, complemented
16	C₅×#5514	C₂	1	2	yes	maximal, complemented
17	C₂×C₅×#892	C₂	1	2	yes	maximal, complemented
18	C₅×#3475	—	3	1	no	maximal, Hall
19	C₂×C₅×#239	C₂²	1	1	yes	characteristic
20	C₂×C₅×#237	C₂²	1	2	yes	—
21	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
23	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×#125	C₂²	1	2	yes	complemented
25	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
26	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
29	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₅×#947	C₂²	1	4	yes	complemented
32	C₅×#946	C₂²	1	2	yes	—
33	C₅×#946	C₂²	1	2	yes	complemented
34	C₅×Q₈×Dic₃	C₂²	1	2	yes	complemented
35	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
36	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
37	C₅×#930	C₂²	1	4	yes	—
38	C₅×#930	C₂²	1	2	yes	complemented
39	C₄×C₅×#67	C₂²	1	2	yes	—
40	C₄×C₅×#67	C₂²	1	4	yes	complemented
41	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
42	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
43	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	complemented
44	C₅×#898	C₂²	1	4	yes	complemented
45	C₅×#898	C₂²	1	4	yes	complemented
46	C₅×#898	C₂²	1	4	yes	complemented
47	C₅×#897	C₂²	1	2	yes	—
48	C₅×#897	C₂²	1	2	yes	complemented
49	C₅×#895	C₂²	1	2	yes	—
50	C₅×#895	C₂²	1	2	yes	complemented
51	C₅×#894	C₂²	1	4	yes	—
52	C₅×#894	C₂²	1	4	yes	complemented
53	C₅×#893	C₂²	1	1	yes	characteristic
54	C₅×#893	C₂²	1	2	yes	—
55	C₅×#893	C₂²	1	4	yes	complemented
56	C₅×#893	C₂²	1	1	yes	characteristic, complemented
57	C₅×#892	C₂²	1	4	yes	—
58	C₅×#892	C₂²	1	2	yes	—
59	C₅×#892	C₂²	1	1	yes	characteristic
60	C₅×#892	C₂²	1	4	yes	complemented
61	C₅×#892	C₂²	1	2	yes	complemented
62	C₅×#892	C₂²	1	2	yes	complemented
63	C₅×#892	C₂²	1	2	yes	complemented
64	C₅×#892	C₂²	1	2	yes	complemented
65	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
66	C₅×#890	C₂²	1	4	yes	complemented
67	C₅×#890	C₂²	1	2	yes	complemented
68	C₅×#887	C₂²	1	2	yes	complemented
69	C₅×#886	C₂²	1	4	yes	—
70	C₅×#886	C₂²	1	4	yes	complemented
71	C₅×#882	C₂²	1	4	yes	—
72	C₅×#67⋊C₄	C₂²	1	2	yes	—
73	C₅×#67⋊C₄	C₂²	1	4	yes	complemented
74	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
75	C₅×#877	C₂²	1	4	yes	complemented
76	C₅×#875	C₂²	1	2	yes	—
77	C₄×C₅×D₁₂	C₂²	1	2	yes	—
78	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
79	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
80	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
81	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
82	C₅×#869	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
84	#86922	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
85	C₅×#556	—	3	1	no	—
86	C₅×#555	—	3	1	no	—
87	C₅×#554	D₃	1	1	yes	characteristic, complemented
88	C₅×#553	—	3	2	no	—
89	C₅×#552	—	3	2	no	—
90	C₅×#552	—	3	2	no	—
91	C₅×#551	—	3	4	no	—
92	C₅×#547	—	3	1	no	—
93	C₅×#546	—	3	2	no	—
94	C₅×#533	—	3	1	no	—
95	C₅×#529	—	3	2	no	—
96	C₅×#529	—	3	4	no	—
97	C₅×#525	—	3	2	no	—
98	C₄×C₅×#41	—	3	1	no	—
99	C₄×C₅×#41	—	3	2	no	—
100	C₂×C₄×C₅×D₄	—	3	1	no	—
101	C₂×C₅×#117	—	3	2	no	—
102	C₂³×C₅×D₃	C₂³	1	2	yes	—
103	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
105	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
107	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
108	C₂×C₅×#67	C₂³	1	2	yes	—
109	C₂×C₅×#67	C₂³	1	4	yes	—
110	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
111	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
112	C₅×#239	—	2	4	no	—
113	C₅×#237	—	2	8	no	—
114	C₅×D₃×D₄	—	2	4	no	—
115	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
116	C₂×C₅×D₁₂	C₂³	1	2	yes	—
117	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
118	C₂×C₅×D₁₂	C₂³	1	4	yes	—
119	C₂×C₄×C₅×D₃	—	2	8	no	—
120	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
121	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
122	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
123	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
124	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
125	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
126	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
127	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
128	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
129	C₂×C₅×Dic₆	C₂³	1	2	yes	—
130	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
131	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
133	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
136	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
137	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₃×C₄²×C₅	C₂³	1	2	yes	—
140	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
141	C₅×#217	C₂³	1	2	yes	—
142	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
143	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
144	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
145	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
146	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
147	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
148	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
149	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
150	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
151	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
152	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
153	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
155	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
156	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
157	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
158	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
159	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
160	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
161	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
162	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
163	C₄×C₅×Dic₃	C₂³	1	4	yes	—
164	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
165	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
166	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
167	C₄×C₅×Dic₃	C₂³	1	2	yes	—
168	C₄×C₅×Dic₃	C₂³	1	2	yes	—
169	C₄×C₅×Dic₃	C₂³	1	4	yes	—
170	C₄×C₅×Dic₃	C₂³	1	4	yes	—
171	C₃×#554	C₂×C₅	1	1	yes	characteristic, complemented
172	#5734	C₂×C₅	1	1	yes	characteristic, complemented
173	#5728	C₂×C₅	1	1	yes	characteristic, complemented
174	#5694	C₂×C₅	1	2	yes	complemented
175	#5691	C₂×C₅	1	2	yes	complemented
176	#5642	C₂×C₅	1	2	yes	complemented
177	#5637	C₂×C₅	1	4	yes	complemented
178	#5627	C₂×C₅	1	2	yes	complemented
179	#5624	C₂×C₅	1	4	yes	complemented
180	#5584	C₂×C₅	1	1	yes	characteristic, complemented
181	C₄×#239	C₂×C₅	1	1	yes	characteristic, complemented
182	#5555	C₂×C₅	1	1	yes	characteristic, complemented
183	#5554	C₂×C₅	1	2	yes	complemented
184	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
185	C₄×#237	C₂×C₅	1	2	yes	complemented
186	#5514	C₂×C₅	1	2	yes	complemented
187	C₂×#892	C₂×C₅	1	2	yes	complemented
188	C₂×C₅×#41	—	3	1	no	—
189	C₂×C₅×#41	—	3	2	no	—
190	C₂²×C₅×D₄	—	3	1	no	—
191	C₂³×C₄×C₅	—	3	2	no	—
192	C₅×C₄⋊Q₈	—	3	1	no	—
193	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
194	C₅×#126	—	3	4	no	—
195	C₅×#126	—	3	4	no	—
196	C₅×#126	—	3	4	no	—
197	C₅×#125	—	3	4	no	—
198	C₅×#125	—	3	2	no	—
199	C₅×#125	C₂×D₃	1	2	yes	complemented
200	C₅×#124	—	3	4	no	—
201	C₅×#124	—	3	2	no	—
202	C₅×#123	—	3	4	no	—
203	C₅×#123	—	3	4	no	—
204	C₅×#123	—	3	4	no	—
205	C₅×#123	—	3	4	no	—
206	C₅×C₂²⋊Q₈	—	3	2	no	—
207	C₅×C₂²⋊Q₈	—	3	2	no	—
208	C₅×C₂²⋊Q₈	—	3	2	no	—
209	C₅×C₂²⋊Q₈	—	3	2	no	—
210	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
211	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
212	C₅×#121	—	3	4	no	—
213	C₅×#121	—	3	2	no	—
214	C₅×#121	—	3	2	no	—
215	C₅×#121	—	3	2	no	—
216	C₅×#120	—	3	4	no	—
217	C₄×C₅×Q₈	—	3	1	no	—
218	C₄×C₅×Q₈	—	3	2	no	—
219	C₄×C₅×Q₈	—	3	2	no	—
220	C₄×C₅×Q₈	—	3	2	no	—
221	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
222	C₄×C₅×D₄	—	3	1	no	—
223	C₄×C₅×D₄	—	3	2	no	—
224	C₄×C₅×D₄	—	3	4	no	—
225	C₄×C₅×D₄	—	3	1	no	—
226	C₄×C₅×D₄	—	3	2	no	—
227	C₄×C₅×D₄	—	3	1	no	—
228	C₄×C₅×D₄	—	3	4	no	—
229	C₄×C₅×D₄	—	3	2	no	—
230	C₄×C₅×D₄	—	3	4	no	—
231	C₄×C₅×D₄	—	3	1	no	—
232	C₄×C₅×D₄	—	3	2	no	—
233	C₄×C₅×D₄	—	3	1	no	—
234	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
235	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
236	C₅×#117	—	3	1	no	—
237	C₅×#117	—	3	2	no	—
238	C₅×#117	—	3	4	no	—
239	C₅×#117	—	3	4	no	—
240	C₅×#117	—	3	2	no	—
241	C₅×#117	—	3	2	no	—
242	C₅×#117	—	3	2	no	—
243	C₅×#117	—	3	2	no	—
244	C₅×#117	—	3	4	no	—
245	C₂×C₅×C₄⋊C₄	—	3	2	no	—
246	C₂×C₅×C₄⋊C₄	—	3	1	no	—
247	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
248	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
249	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
250	C₂×C₄²×C₅	—	3	4	no	—
251	C₂×C₄²×C₅	—	3	1	no	—
252	C₂×C₄²×C₅	—	3	2	no	—
253	#3475	—	3	1	no	Sylow
254	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
255	C₂²×C₅×D₃	—	2	4	no	—
256	C₂²×C₅×D₃	—	2	4	no	—
257	C₂²×C₅×D₃	—	4	2	no	—
258	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
259	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
260	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
261	C₃×C₅×Q₈	—	2	2	no	—
262	C₃×C₅×Q₈	—	4	2	no	—
263	C₃×C₅×D₄	#41	1	4	yes	complemented
264	C₂×C₃×C₄×C₅	—	2	4	no	—
265	C₂×C₃×C₄×C₅	—	4	4	no	—
266	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
267	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
268	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
269	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
271	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
273	C₅×#67	—	2	4	no	—
274	C₅×#67	—	2	8	no	—
275	C₂×C₅×Dic₃	—	2	8	no	—
276	C₂×C₅×Dic₃	—	2	4	no	—
277	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
278	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
279	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
280	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
281	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
282	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
283	C₅×D₁₂	—	2	4	no	—
284	C₅×D₁₂	—	2	2	no	—
285	C₅×D₁₂	—	2	2	no	—
286	C₅×D₁₂	—	4	4	no	—
287	C₄×C₅×D₃	—	2	4	no	—
288	C₄×C₅×D₃	—	2	4	no	—
289	C₄×C₅×D₃	—	2	2	no	—
290	C₄×C₅×D₃	—	2	4	no	—
291	C₄×C₅×D₃	—	2	4	no	—
292	C₄×C₅×D₃	—	2	4	no	—
293	C₄×C₅×D₃	—	4	2	no	—
294	C₄×C₅×D₃	—	4	1	no	—
295	C₄×C₅×D₃	#41	1	4	yes	complemented
296	C₅×Dic₆	—	2	4	no	—
297	C₂×#239	C₂²×C₅	1	1	yes	characteristic
298	C₂×#237	C₂²×C₅	1	2	yes	—
299	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
300	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
301	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
302	C₃×#125	C₂²×C₅	1	2	yes	complemented
303	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
304	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
305	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
306	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
307	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
308	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
309	#947	C₂²×C₅	1	4	yes	complemented
310	#946	C₂²×C₅	1	2	yes	—
311	#946	C₂²×C₅	1	2	yes	complemented
312	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
313	Q₈×Dic₃	C₂²×C₅	1	2	yes	complemented
314	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
315	#930	C₂²×C₅	1	4	yes	—
316	#930	C₂²×C₅	1	2	yes	complemented
317	C₄×#67	C₂²×C₅	1	2	yes	—
318	C₄×#67	C₂²×C₅	1	4	yes	complemented
319	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
320	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
321	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	complemented
322	#898	C₂²×C₅	1	4	yes	complemented
323	#898	C₂²×C₅	1	4	yes	complemented
324	#898	C₂²×C₅	1	4	yes	complemented
325	#897	C₂²×C₅	1	2	yes	—
326	#897	C₂²×C₅	1	2	yes	complemented
327	#895	C₂²×C₅	1	2	yes	—
328	#895	C₂²×C₅	1	2	yes	complemented
329	#894	C₂²×C₅	1	4	yes	—
330	#894	C₂²×C₅	1	4	yes	complemented
331	#893	C₂²×C₅	1	2	yes	—
332	#893	C₂²×C₅	1	1	yes	characteristic
333	#893	C₂²×C₅	1	4	yes	complemented
334	#893	C₂²×C₅	1	1	yes	characteristic, complemented
335	#892	C₂²×C₅	1	4	yes	—
336	#892	C₂²×C₅	1	2	yes	—
337	#892	C₂²×C₅	1	1	yes	characteristic
338	#892	C₂²×C₅	1	2	yes	complemented
339	#892	C₂²×C₅	1	4	yes	complemented
340	#892	C₂²×C₅	1	2	yes	complemented
341	#892	C₂²×C₅	1	2	yes	complemented
342	#892	C₂²×C₅	1	2	yes	complemented
343	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
344	#890	C₂²×C₅	1	4	yes	complemented
345	#890	C₂²×C₅	1	2	yes	complemented
346	#887	C₂²×C₅	1	2	yes	complemented
347	#886	C₂²×C₅	1	4	yes	—
348	#886	C₂²×C₅	1	4	yes	complemented
349	#882	C₂²×C₅	1	4	yes	—
350	#67⋊C₄	C₂²×C₅	1	2	yes	—
351	#67⋊C₄	C₂²×C₅	1	4	yes	complemented
352	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
353	#877	C₂²×C₅	1	4	yes	complemented
354	#875	C₂²×C₅	1	2	yes	—
355	C₄×D₁₂	C₂²×C₅	1	2	yes	—
356	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
357	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
358	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
359	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
360	#869	C₂²×C₅	1	1	yes	characteristic, complemented
361	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
362	C₂⁴×C₅	—	3	2	no	—
363	C₅×#41	—	6	4	no	—
364	C₅×#41	—	6	8	no	—
365	C₂×C₅×Q₈	—	3	2	no	—
366	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
367	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
368	C₂×C₅×D₄	—	3	4	no	—
369	C₂×C₅×D₄	—	3	2	no	—
370	C₂×C₅×D₄	—	3	2	no	—
371	C₂×C₅×D₄	—	3	1	no	—
372	C₂×C₅×D₄	—	3	1	no	—
373	C₂×C₅×D₄	—	3	4	no	—
374	C₂×C₅×D₄	—	6	4	no	—
375	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
376	C₂²×C₄×C₅	—	3	1	no	—
377	C₂²×C₄×C₅	—	3	2	no	—
378	C₂²×C₄×C₅	—	3	4	no	—
379	C₂²×C₄×C₅	—	3	1	no	—
380	C₂²×C₄×C₅	—	3	2	no	—
381	C₂²×C₄×C₅	—	3	2	no	—
382	C₂²×C₄×C₅	—	3	2	no	—
383	C₂²×C₄×C₅	—	3	2	no	—
384	C₂²×C₄×C₅	—	3	2	no	—
385	C₂²×C₄×C₅	—	3	1	no	—
386	C₂²×C₄×C₅	—	3	2	no	—
387	C₂²×C₄×C₅	—	6	8	no	—
388	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
389	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
390	C₅×C₄⋊C₄	—	3	1	no	—
391	C₅×C₄⋊C₄	—	3	1	no	—
392	C₅×C₄⋊C₄	—	3	2	no	—
393	C₅×C₄⋊C₄	—	3	4	no	—
394	C₅×C₄⋊C₄	—	3	2	no	—
395	C₅×C₄⋊C₄	—	3	4	no	—
396	C₅×C₄⋊C₄	—	3	4	no	—
397	C₅×C₄⋊C₄	—	3	2	no	—
398	C₅×C₄⋊C₄	—	3	4	no	—
399	C₅×C₄⋊C₄	—	3	2	no	—
400	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
401	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
402	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
403	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
404	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
405	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
406	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
407	C₅×C₂²⋊C₄	—	3	2	no	—
408	C₅×C₂²⋊C₄	—	3	2	no	—
409	C₅×C₂²⋊C₄	—	3	4	no	—
410	C₅×C₂²⋊C₄	—	3	4	no	—
411	C₅×C₂²⋊C₄	—	3	4	no	—
412	C₅×C₂²⋊C₄	—	3	2	no	—
413	C₅×C₂²⋊C₄	—	3	2	no	—
414	C₅×C₂²⋊C₄	—	3	2	no	—
415	C₅×C₂²⋊C₄	—	3	4	no	—
416	C₅×C₂²⋊C₄	—	3	2	no	—
417	C₅×C₂²⋊C₄	—	3	4	no	—
418	C₅×C₂²⋊C₄	—	3	4	no	—
419	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
420	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
421	C₄²×C₅	—	3	2	no	—
422	C₄²×C₅	—	3	1	no	—
423	C₄²×C₅	—	3	4	no	—
424	C₄²×C₅	—	3	4	no	—
425	C₄²×C₅	—	3	1	no	—
426	C₄²×C₅	—	3	2	no	—
427	C₄²×C₅	—	3	4	no	—
428	C₄²×C₅	—	3	1	no	—
429	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
430	C₄²×C₅	C₂²×D₃	1	2	yes	—
431	#556	—	3	1	no	—
432	#555	—	3	1	no	—
433	#554	C₅×D₃	1	1	yes	characteristic, complemented
434	#553	—	3	2	no	—
435	#552	—	3	2	no	—
436	#552	—	3	2	no	—
437	#551	—	3	4	no	—
438	#547	—	3	1	no	—
439	#546	—	3	2	no	—
440	#533	—	3	1	no	—
441	#529	—	3	2	no	—
442	#529	—	3	4	no	—
443	#525	—	3	2	no	—
444	C₄×#41	—	3	1	no	—
445	C₄×#41	—	3	2	no	—
446	C₂×C₄×D₄	—	3	1	no	—
447	C₂×#117	—	3	2	no	—
448	C₂²×C₃×C₅	—	2	2	no	—
449	C₂²×C₃×C₅	—	2	2	no	—
450	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
451	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
452	C₂×C₅×D₃	—	2	1	no	—
453	C₂×C₅×D₃	—	2	1	no	—
454	C₂×C₅×D₃	—	2	2	no	—
455	C₂×C₅×D₃	—	2	2	no	—
456	C₂×C₅×D₃	—	2	2	no	—
457	C₂×C₅×D₃	—	2	2	no	—
458	C₂×C₅×D₃	—	2	2	no	—
459	C₂×C₅×D₃	—	2	2	no	—
460	C₂×C₅×D₃	—	4	8	no	—
461	C₂×C₅×D₃	C₂×#41	1	2	yes	—
462	C₃×C₄×C₅	—	2	2	no	—
463	C₃×C₄×C₅	—	2	2	no	—
464	C₃×C₄×C₅	—	2	2	no	—
465	C₃×C₄×C₅	—	2	1	no	—
466	C₃×C₄×C₅	—	2	4	no	—
467	C₃×C₄×C₅	C₂×#41	1	2	yes	—
468	C₃×C₄×C₅	C₂×#41	1	2	yes	—
469	C₅×Dic₃	—	2	4	no	—
470	C₅×Dic₃	—	2	2	no	—
471	C₅×Dic₃	—	2	2	no	—
472	C₅×Dic₃	—	2	1	no	—
473	C₅×Dic₃	—	2	1	no	—
474	C₅×Dic₃	C₂×#41	1	2	yes	—
475	C₂³×D₃	C₂³×C₅	1	2	yes	—
476	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
477	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
478	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
479	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
480	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
481	C₂×#67	C₂³×C₅	1	2	yes	—
482	C₂×#67	C₂³×C₅	1	4	yes	—
483	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
484	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
485	#239	—	2	4	no	—
486	#237	—	2	8	no	—
487	D₃×D₄	—	2	4	no	—
488	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
489	C₂×D₁₂	C₂³×C₅	1	2	yes	—
490	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
491	C₂×D₁₂	C₂³×C₅	1	4	yes	—
492	C₂×C₄×D₃	—	2	8	no	—
493	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
494	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
495	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
496	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
497	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
498	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
499	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
500	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
501	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
502	C₂×Dic₆	C₂³×C₅	1	2	yes	—
503	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
504	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
505	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
506	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
507	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
508	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
509	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
510	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
511	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
512	C₃×C₄²	C₂³×C₅	1	2	yes	—
513	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
514	#217	C₂³×C₅	1	2	yes	—
515	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
516	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
517	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
518	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
519	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
520	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
521	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
522	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
523	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
524	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
525	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
526	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
527	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
528	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
529	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
530	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
531	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
532	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
533	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
534	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
535	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
536	C₄×Dic₃	C₂³×C₅	1	4	yes	—
537	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
538	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
539	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
540	C₄×Dic₃	C₂³×C₅	1	2	yes	—
541	C₄×Dic₃	C₂³×C₅	1	2	yes	—
542	C₄×Dic₃	C₂³×C₅	1	4	yes	—
543	C₄×Dic₃	C₂³×C₅	1	4	yes	—
544	C₂³×C₅	—	3	1	no	—
545	C₂³×C₅	—	3	2	no	—
546	C₂³×C₅	—	3	2	no	—
547	C₂³×C₅	—	6	4	no	—
548	C₂³×C₅	—	6	4	no	—
549	C₂³×C₅	—	12	2	no	—
550	C₂³×C₅	C₂³×D₃	1	2	yes	—
551	C₅×Q₈	—	2	2	no	—
552	C₅×Q₈	—	4	2	no	—
553	C₅×Q₈	—	6	4	no	—
554	C₅×D₄	—	6	4	no	—
555	C₅×D₄	—	6	4	no	—
556	C₅×D₄	—	6	8	no	—
557	C₅×D₄	—	6	2	no	—
558	C₅×D₄	—	6	2	no	—
559	C₅×D₄	—	12	4	no	—
560	C₅×D₄	#239	1	4	yes	complemented
561	C₂×C₄×C₅	—	2	4	no	—
562	C₂×C₄×C₅	—	3	1	no	—
563	C₂×C₄×C₅	—	3	4	no	—
564	C₂×C₄×C₅	—	3	2	no	—
565	C₂×C₄×C₅	—	3	2	no	—
566	C₂×C₄×C₅	—	3	1	no	—
567	C₂×C₄×C₅	—	3	4	no	—
568	C₂×C₄×C₅	—	3	1	no	—
569	C₂×C₄×C₅	—	4	4	no	—
570	C₂×C₄×C₅	—	6	4	no	—
571	C₂×C₄×C₅	—	6	4	no	—
572	C₂×C₄×C₅	—	6	4	no	—
573	C₂×C₄×C₅	—	6	4	no	—
574	C₂×C₄×C₅	—	6	8	no	—
575	C₂×C₄×C₅	—	6	2	no	—
576	C₂×C₄×C₅	—	6	4	no	—
577	C₂×C₄×C₅	—	6	4	no	—
578	C₂×C₄×C₅	—	12	2	no	—
579	C₂×C₄×C₅	—	12	1	no	—
580	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
581	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
582	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
583	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
584	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
585	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
586	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
587	C₂×#41	—	3	1	no	—
588	C₂×#41	—	3	2	no	—
589	C₂²×D₄	—	3	1	no	—
590	C₂³×C₄	—	3	2	no	—
591	C₄⋊Q₈	—	3	1	no	—
592	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
593	#126	—	3	4	no	—
594	#126	—	3	4	no	—
595	#126	—	3	4	no	—
596	#125	—	3	4	no	—
597	#125	—	3	2	no	—
598	#125	C₂×C₅×D₃	1	2	yes	complemented
599	#124	—	3	4	no	—
600	#124	—	3	2	no	—
601	#123	—	3	4	no	—
602	#123	—	3	4	no	—
603	#123	—	3	4	no	—
604	#123	—	3	4	no	—
605	C₂²⋊Q₈	—	3	2	no	—
606	C₂²⋊Q₈	—	3	2	no	—
607	C₂²⋊Q₈	—	3	2	no	—
608	C₂²⋊Q₈	—	3	2	no	—
609	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
610	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
611	#121	—	3	2	no	—
612	#121	—	3	4	no	—
613	#121	—	3	2	no	—
614	#121	—	3	2	no	—
615	#120	—	3	4	no	—
616	C₄×Q₈	—	3	1	no	—
617	C₄×Q₈	—	3	2	no	—
618	C₄×Q₈	—	3	2	no	—
619	C₄×Q₈	—	3	2	no	—
620	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
621	C₄×D₄	—	3	1	no	—
622	C₄×D₄	—	3	2	no	—
623	C₄×D₄	—	3	4	no	—
624	C₄×D₄	—	3	1	no	—
625	C₄×D₄	—	3	2	no	—
626	C₄×D₄	—	3	1	no	—
627	C₄×D₄	—	3	4	no	—
628	C₄×D₄	—	3	2	no	—
629	C₄×D₄	—	3	4	no	—
630	C₄×D₄	—	3	1	no	—
631	C₄×D₄	—	3	2	no	—
632	C₄×D₄	—	3	1	no	—
633	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
634	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
635	#117	—	3	1	no	—
636	#117	—	3	2	no	—
637	#117	—	3	4	no	—
638	#117	—	3	4	no	—
639	#117	—	3	2	no	—
640	#117	—	3	2	no	—
641	#117	—	3	2	no	—
642	#117	—	3	2	no	—
643	#117	—	3	4	no	—
644	C₂×C₄⋊C₄	—	3	2	no	—
645	C₂×C₄⋊C₄	—	3	1	no	—
646	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
647	C₂×C₂²⋊C₄	—	3	4	no	—
648	C₂×C₂²⋊C₄	—	3	2	no	—
649	C₂×C₄²	—	3	4	no	—
650	C₂×C₄²	—	3	1	no	—
651	C₂×C₄²	—	3	2	no	—
652	C₂×C₃×C₅	—	2	4	no	—
653	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
654	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
655	C₂×C₃×C₅	#585	1	1	yes	characteristic
656	C₅×D₃	—	2	2	no	—
657	C₅×D₃	—	4	2	no	—
658	C₅×D₃	—	4	2	no	—
659	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
660	C₂²×D₃	—	2	4	no	—
661	C₂²×D₃	—	2	4	no	—
662	C₂²×D₃	—	4	2	no	—
663	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
664	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
665	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
666	C₃×Q₈	—	2	2	no	—
667	C₃×Q₈	—	4	2	no	—
668	C₃×D₄	C₅×#41	1	4	yes	complemented
669	C₂×C₃×C₄	—	2	4	no	—
670	C₂×C₃×C₄	—	4	4	no	—
671	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
672	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
673	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
674	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
675	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
676	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
677	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
678	#67	—	2	4	no	—
679	#67	—	2	8	no	—
680	C₂×Dic₃	—	2	8	no	—
681	C₂×Dic₃	—	2	4	no	—
682	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
683	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
684	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
685	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
686	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
687	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
688	D₁₂	—	2	4	no	—
689	D₁₂	—	2	2	no	—
690	D₁₂	—	2	2	no	—
691	D₁₂	—	4	4	no	—
692	C₄×D₃	—	2	4	no	—
693	C₄×D₃	—	2	4	no	—
694	C₄×D₃	—	2	2	no	—
695	C₄×D₃	—	2	4	no	—
696	C₄×D₃	—	2	4	no	—
697	C₄×D₃	—	2	4	no	—
698	C₄×D₃	—	4	2	no	—
699	C₄×D₃	—	4	1	no	—
700	C₄×D₃	C₅×#41	1	4	yes	complemented
701	Dic₆	—	2	4	no	—
702	C₂²×C₅	—	2	2	no	—
703	C₂²×C₅	—	2	2	no	—
704	C₂²×C₅	—	3	2	no	—
705	C₂²×C₅	—	6	1	no	—
706	C₂²×C₅	—	6	1	no	—
707	C₂²×C₅	—	6	2	no	—
708	C₂²×C₅	—	6	2	no	—
709	C₂²×C₅	—	6	2	no	—
710	C₂²×C₅	—	6	2	no	—
711	C₂²×C₅	—	6	2	no	—
712	C₂²×C₅	—	6	2	no	—
713	C₂²×C₅	—	12	8	no	—
714	C₂²×C₅	C₂×#239	1	4	yes	—
715	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
716	C₄×C₅	—	2	2	no	—
717	C₄×C₅	—	2	2	no	—
718	C₄×C₅	—	2	2	no	—
719	C₄×C₅	—	2	4	no	—
720	C₄×C₅	—	2	1	no	—
721	C₄×C₅	—	3	2	no	—
722	C₄×C₅	—	6	2	no	—
723	C₄×C₅	—	6	1	no	—
724	C₄×C₅	—	6	4	no	—
725	C₄×C₅	—	6	2	no	—
726	C₄×C₅	—	6	1	no	—
727	C₄×C₅	C₂×#239	1	2	yes	—
728	C₄×C₅	D₃×#41	1	2	yes	—
729	C₂⁴	—	3	2	no	—
730	#41	—	6	4	no	—
731	#41	—	6	8	no	—
732	C₂×Q₈	—	3	2	no	—
733	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
734	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
735	C₂×D₄	—	3	4	no	—
736	C₂×D₄	—	3	2	no	—
737	C₂×D₄	—	3	2	no	—
738	C₂×D₄	—	3	1	no	—
739	C₂×D₄	—	3	1	no	—
740	C₂×D₄	—	3	4	no	—
741	C₂×D₄	—	6	4	no	—
742	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
743	C₂²×C₄	—	3	1	no	—
744	C₂²×C₄	—	3	2	no	—
745	C₂²×C₄	—	3	4	no	—
746	C₂²×C₄	—	3	1	no	—
747	C₂²×C₄	—	3	2	no	—
748	C₂²×C₄	—	3	2	no	—
749	C₂²×C₄	—	3	2	no	—
750	C₂²×C₄	—	3	2	no	—
751	C₂²×C₄	—	3	2	no	—
752	C₂²×C₄	—	3	1	no	—
753	C₂²×C₄	—	3	2	no	—
754	C₂²×C₄	—	6	8	no	—
755	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
756	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
757	C₄⋊C₄	—	3	1	no	—
758	C₄⋊C₄	—	3	1	no	—
759	C₄⋊C₄	—	3	2	no	—
760	C₄⋊C₄	—	3	4	no	—
761	C₄⋊C₄	—	3	2	no	—
762	C₄⋊C₄	—	3	4	no	—
763	C₄⋊C₄	—	3	4	no	—
764	C₄⋊C₄	—	3	2	no	—
765	C₄⋊C₄	—	3	4	no	—
766	C₄⋊C₄	—	3	2	no	—
767	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
770	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
771	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
772	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
773	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
774	C₂²⋊C₄	—	3	2	no	—
775	C₂²⋊C₄	—	3	2	no	—
776	C₂²⋊C₄	—	3	4	no	—
777	C₂²⋊C₄	—	3	4	no	—
778	C₂²⋊C₄	—	3	4	no	—
779	C₂²⋊C₄	—	3	2	no	—
780	C₂²⋊C₄	—	3	2	no	—
781	C₂²⋊C₄	—	3	2	no	—
782	C₂²⋊C₄	—	3	4	no	—
783	C₂²⋊C₄	—	3	2	no	—
784	C₂²⋊C₄	—	3	4	no	—
785	C₂²⋊C₄	—	3	4	no	—
786	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
787	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
788	C₄²	—	3	2	no	—
789	C₄²	—	3	1	no	—
790	C₄²	—	3	4	no	—
791	C₄²	—	3	4	no	—
792	C₄²	—	3	1	no	—
793	C₄²	—	3	2	no	—
794	C₄²	—	3	4	no	—
795	C₄²	—	3	1	no	—
796	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
797	C₄²	C₂²×C₅×D₃	1	2	yes	—
798	C₃×C₅	#3475	1	1	yes	characteristic, complemented, Hall
799	C₂²×C₃	—	2	2	no	—
800	C₂²×C₃	—	2	2	no	—
801	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
802	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
803	C₂×D₃	—	2	1	no	—
804	C₂×D₃	—	2	1	no	—
805	C₂×D₃	—	2	2	no	—
806	C₂×D₃	—	2	2	no	—
807	C₂×D₃	—	2	2	no	—
808	C₂×D₃	—	2	2	no	—
809	C₂×D₃	—	2	2	no	—
810	C₂×D₃	—	2	2	no	—
811	C₂×D₃	—	4	8	no	—
812	C₂×D₃	C₂×C₅×#41	1	2	yes	—
813	C₃×C₄	—	2	2	no	—
814	C₃×C₄	—	2	2	no	—
815	C₃×C₄	—	2	2	no	—
816	C₃×C₄	—	2	1	no	—
817	C₃×C₄	—	2	4	no	—
818	C₃×C₄	C₂×C₅×#41	1	2	yes	—
819	C₃×C₄	C₂×C₅×#41	1	2	yes	—
820	Dic₃	—	2	4	no	—
821	Dic₃	—	2	2	no	—
822	Dic₃	—	2	2	no	—
823	Dic₃	—	2	1	no	—
824	Dic₃	—	2	1	no	—
825	Dic₃	C₂×C₅×#41	1	2	yes	—
826	C₂×C₅	—	2	4	no	—
827	C₂×C₅	—	6	2	no	—
828	C₂×C₅	—	12	2	no	—
829	C₂×C₅	—	12	2	no	—
830	C₂×C₅	C₂²×#239	1	1	yes	characteristic
831	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
832	C₂×C₅	#5966	1	1	yes	characteristic
833	C₂³	—	3	1	no	—
834	C₂³	—	3	2	no	—
835	C₂³	—	3	2	no	—
836	C₂³	—	6	4	no	—
837	C₂³	—	6	4	no	—
838	C₂³	—	12	2	no	—
839	C₂³	C₂³×C₅×D₃	1	2	yes	—
840	Q₈	—	2	2	no	—
841	Q₈	—	4	2	no	—
842	Q₈	—	6	4	no	—
843	D₄	—	6	4	no	—
844	D₄	—	6	4	no	—
845	D₄	—	6	8	no	—
846	D₄	—	6	2	no	—
847	D₄	—	6	2	no	—
848	D₄	—	12	4	no	—
849	D₄	C₅×#239	1	4	yes	complemented
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	3	1	no	—
852	C₂×C₄	—	3	4	no	—
853	C₂×C₄	—	3	2	no	—
854	C₂×C₄	—	3	2	no	—
855	C₂×C₄	—	3	1	no	—
856	C₂×C₄	—	3	4	no	—
857	C₂×C₄	—	3	1	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	6	4	no	—
860	C₂×C₄	—	6	4	no	—
861	C₂×C₄	—	6	4	no	—
862	C₂×C₄	—	6	4	no	—
863	C₂×C₄	—	6	8	no	—
864	C₂×C₄	—	6	2	no	—
865	C₂×C₄	—	6	4	no	—
866	C₂×C₄	—	6	4	no	—
867	C₂×C₄	—	12	2	no	—
868	C₂×C₄	—	12	1	no	—
869	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
870	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
871	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
872	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
873	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
874	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
875	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
876	C₂×C₃	—	2	4	no	—
877	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
878	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
879	C₂×C₃	C₅×#585	1	1	yes	characteristic
880	D₃	—	2	2	no	—
881	D₃	—	4	2	no	—
882	D₃	—	4	2	no	—
883	C₅	#86922	1	1	yes	characteristic, direct product factor, Sylow
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	3	2	no	—
887	C₂²	—	6	1	no	—
888	C₂²	—	6	1	no	—
889	C₂²	—	6	2	no	—
890	C₂²	—	6	2	no	—
891	C₂²	—	6	2	no	—
892	C₂²	—	6	2	no	—
893	C₂²	—	6	2	no	—
894	C₂²	—	6	2	no	—
895	C₂²	—	12	8	no	—
896	C₂²	C₂×C₅×#239	1	4	yes	—
897	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	4	no	—
902	C₄	—	2	1	no	—
903	C₄	—	3	2	no	—
904	C₄	—	6	2	no	—
905	C₄	—	6	1	no	—
906	C₄	—	6	4	no	—
907	C₄	—	6	2	no	—
908	C₄	—	6	1	no	—
909	C₄	C₂×C₅×#239	1	2	yes	—
910	C₄	C₅×D₃×#41	1	2	yes	—
911	C₃	C₅×#3475	1	1	yes	characteristic, complemented, Sylow
912	C₂	—	2	4	no	—
913	C₂	—	6	2	no	—
914	C₂	—	12	2	no	—
915	C₂	—	12	2	no	—
916	C₂	C₂²×C₅×#239	1	1	yes	characteristic
917	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
918	C₂	C₅×#5966	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#554	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#554	D₃
hypocenter	C₃	C₅×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#554

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₅×#554	C₂	semidirect
2. C₅×#5734	C₂	semidirect
3. C₅×#5728	C₂	semidirect
4. C₅×#5694	C₂	semidirect
5. C₅×#5691	C₂	semidirect
6. C₅×#5642	C₂	semidirect
7. C₅×#5637	C₂	semidirect
8. C₅×#5627	C₂	semidirect
9. C₅×#5624	C₂	semidirect
10. C₅×#5584	C₂	semidirect
11. C₄×C₅×#239	C₂	semidirect
12. C₅×#5555	C₂	semidirect
13. C₅×#5554	C₂	semidirect
14. C₄×C₅×D₃×D₄	C₂	semidirect
15. C₄×C₅×#237	C₂	semidirect
16. C₅×#5514	C₂	semidirect
17. C₂×C₅×#892	C₂	semidirect
23. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
24. C₃×C₅×#125	C₂²	semidirect
25. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
26. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
27. C₃×C₄×C₅×Q₈	C₂²	semidirect
30. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
31. C₅×#947	C₂²	semidirect
33. C₅×#946	C₂²	semidirect
34. C₅×Q₈×Dic₃	C₂²	semidirect
35. C₅×Q₈×Dic₃	C₂²	semidirect
38. C₅×#930	C₂²	semidirect
40. C₄×C₅×#67	C₂²	semidirect
42. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
43. C₂×C₄×C₅×Dic₃	C₂²	semidirect
44. C₅×#898	C₂²	semidirect
45. C₅×#898	C₂²	semidirect
46. C₅×#898	C₂²	semidirect
48. C₅×#897	C₂²	semidirect
50. C₅×#895	C₂²	semidirect
52. C₅×#894	C₂²	semidirect
55. C₅×#893	C₂²	semidirect
56. C₅×#893	C₂²	semidirect
60. C₅×#892	C₂²	semidirect
61. C₅×#892	C₂²	semidirect
62. C₅×#892	C₂²	semidirect
63. C₅×#892	C₂²	semidirect
64. C₅×#892	C₂²	semidirect
66. C₅×#890	C₂²	semidirect
67. C₅×#890	C₂²	semidirect
68. C₅×#887	C₂²	semidirect
70. C₅×#886	C₂²	semidirect
73. C₅×#67⋊C₄	C₂²	semidirect
75. C₅×#877	C₂²	semidirect
79. C₄×C₅×D₁₂	C₂²	semidirect
81. C₄²×C₅×D₃	C₂²	semidirect
82. C₅×#869	C₂²	semidirect
83. C₄×C₅×Dic₆	C₂²	semidirect
84. #86922	C₅	direct (N × H)
87. C₅×#554	D₃	semidirect
171. C₃×#554	C₂×C₅	semidirect
172. #5734	C₂×C₅	semidirect
173. #5728	C₂×C₅	semidirect
174. #5694	C₂×C₅	semidirect
175. #5691	C₂×C₅	semidirect
176. #5642	C₂×C₅	semidirect
177. #5637	C₂×C₅	semidirect
178. #5627	C₂×C₅	semidirect
179. #5624	C₂×C₅	semidirect
180. #5584	C₂×C₅	semidirect
181. C₄×#239	C₂×C₅	semidirect
182. #5555	C₂×C₅	semidirect
183. #5554	C₂×C₅	semidirect
184. C₄×D₃×D₄	C₂×C₅	semidirect
185. C₄×#237	C₂×C₅	semidirect
186. #5514	C₂×C₅	semidirect
187. C₂×#892	C₂×C₅	semidirect
193. C₅×C₄⋊Q₈	C₂×D₃	semidirect
199. C₅×#125	C₂×D₃	semidirect
210. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
211. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
221. C₄×C₅×Q₈	C₂×D₃	semidirect
247. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
263. C₃×C₅×D₄	#41	semidirect
295. C₄×C₅×D₃	#41	semidirect
301. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
302. C₃×#125	C₂²×C₅	semidirect
303. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
304. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
305. C₃×C₄×Q₈	C₂²×C₅	semidirect
308. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
309. #947	C₂²×C₅	semidirect
311. #946	C₂²×C₅	semidirect
312. Q₈×Dic₃	C₂²×C₅	semidirect
313. Q₈×Dic₃	C₂²×C₅	semidirect
316. #930	C₂²×C₅	semidirect
318. C₄×#67	C₂²×C₅	semidirect
320. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
321. C₂×C₄×Dic₃	C₂²×C₅	semidirect
322. #898	C₂²×C₅	semidirect
323. #898	C₂²×C₅	semidirect
324. #898	C₂²×C₅	semidirect
326. #897	C₂²×C₅	semidirect
328. #895	C₂²×C₅	semidirect
330. #894	C₂²×C₅	semidirect
333. #893	C₂²×C₅	semidirect
334. #893	C₂²×C₅	semidirect
338. #892	C₂²×C₅	semidirect
339. #892	C₂²×C₅	semidirect
340. #892	C₂²×C₅	semidirect
341. #892	C₂²×C₅	semidirect
342. #892	C₂²×C₅	semidirect
344. #890	C₂²×C₅	semidirect
345. #890	C₂²×C₅	semidirect
346. #887	C₂²×C₅	semidirect
348. #886	C₂²×C₅	semidirect
351. #67⋊C₄	C₂²×C₅	semidirect
353. #877	C₂²×C₅	semidirect
357. C₄×D₁₂	C₂²×C₅	semidirect
359. C₄²×D₃	C₂²×C₅	semidirect
360. #869	C₂²×C₅	semidirect
361. C₄×Dic₆	C₂²×C₅	semidirect
433. #554	C₅×D₃	semidirect
560. C₅×D₄	#239	semidirect
592. C₄⋊Q₈	C₂×C₅×D₃	semidirect
598. #125	C₂×C₅×D₃	semidirect
609. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
610. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
620. C₄×Q₈	C₂×C₅×D₃	semidirect
646. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
668. C₃×D₄	C₅×#41	semidirect
700. C₄×D₃	C₅×#41	semidirect
798. C₃×C₅	#3475	semidirect
849. D₄	C₅×#239	semidirect
883. C₅	#86922	direct (N × H)
911. C₃	C₅×#3475	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#554	2
C₅×#5734	2
C₅×#5728	2
C₅×#5694	2
C₅×#5691	2
C₅×#5642	2
C₅×#5637	2
C₅×#5627	2
C₅×#5624	2
C₅×#5584	2
C₄×C₅×#239	2
C₅×#5555	2
C₅×#5554	2
C₄×C₅×D₃×D₄	2
C₄×C₅×#237	2
C₅×#5514	2
C₂×C₅×#892	2
C₅×#3475	3
#86922	5

Subgroups — C5×#86922 #14484153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86922 #14484153